Topological defects in 1D elastic waves

It has been recently shown theoretically that a topological defect in a 1D periodic potential may give rise to two localized states within the energy gaps. In this work we present an experimental realization of this effect for the case of torsional waves in elastic rods. We also show numerically that three, or even more, localized states can be present if the parameters characterizing the topological defect are suitably varied.Comment: 3 pages, 4 figures, accepted in Physica

Analytic Non-integrability in String Theory

Using analytic techniques developed for Hamiltonian dynamical systems we show that a certain classical string configurations in AdS_5 x X_5 with X_5 in a large class of Einstein spaces, is non-integrable. This answers the question of integrability of string on such backgrounds in the negative. We consider a string localized in the center of AdS_5 that winds around two circles in the manifold X_5.Comment: 14 page

Nonautonomous Hamiltonian Systems and Morales-Ramis Theory I. The Case x¨=f(x,t)\ddot{x}=f(x,t)

In this paper we present an approach towards the comprehensive analysis of the non-integrability of differential equations in the form $\ddot x=f(x,t)$ which is analogous to Hamiltonian systems with 1+1/2 degree of freedom. In particular, we analyze the non-integrability of some important families of differential equations such as Painlev\'e II, Sitnikov and Hill-Schr\"odinger equation. We emphasize in Painlev\'e II, showing its non-integrability through three different Hamiltonian systems, and also in Sitnikov in which two different version including numerical results are shown. The main tool to study the non-integrability of these kind of Hamiltonian systems is Morales-Ramis theory. This paper is a very slight improvement of the talk with the almost-same title delivered by the author in SIAM Conference on Applications of Dynamical Systems 2007.Comment: 15 pages without figures (19 pages and 6 figures in the published version

Using dissolved oxygen concentrations to determine mixed layer depths in the Bellingshausen Sea

Concentrations of oxygen (O<sub>2</sub>) and other dissolved gases in the oceanic mixed layer are often used to calculate air-sea gas exchange fluxes. The mixed layer depth (<i>z</i><sub>mix</sub>) may be defined using criteria based on temperature or density differences to a reference depth near the ocean surface. However, temperature criteria fail in regions with strong haloclines such as the Southern Ocean where heat, freshwater and momentum fluxes interact to establish mixed layers. Moreover, the time scales of air-sea exchange differ for gases and heat, so that <i>z</i><sub>mix</sub> defined using oxygen may be different than <i>z</i><sub>mix</sub> defined using temperature or density. Here, we propose to define an O<sub>2</sub>-based mixed layer depth, <i>z</i><sub>mix</sub>(O<sub>2</sub>), as the depth where the relative difference between the O<sub>2</sub> concentration and a reference value at a depth equivalent to 10 dbar equals 0.5 %. This definition was established by analysis of O<sub>2</sub> profiles from the Bellingshausen Sea (west of the Antarctic Peninsula) and corroborated by visual inspection. Comparisons of <i>z</i><sub>mix</sub>(O<sub>2</sub>) with <i>z</i><sub>mix</sub> based on potential temperature differences, i.e., <i>z</i><sub>mix</sub>(0.2 °C) and <i>z</i><sub>mix</sub>(0.5 °C), and potential density differences, i.e., <i>z</i><sub>mix</sub>(0.03 kg m<sup>−3</sup>) and <i>z</i><sub>mix</sub>(0.125 kg m<sup>−3</sup>), showed that <i>z</i><sub>mix</sub>(O<sub>2</sub>) closely follows <i>z</i><sub>mix</sub>(0.03 kg m<sup>−3</sup>). Further comparisons with published <i>z</i><sub>mix</sub> climatologies and <i>z</i><sub>mix</sub> derived from World Ocean Atlas 2005 data were also performed. To establish <i>z</i><sub>mix</sub> for use with biological production estimates in the absence of O<sub>2</sub> profiles, we suggest using <i>z</i><sub>mix</sub>(0.03 kg m<sup>−3</sup>), which is also the basis for the climatology by de Boyer Montégut et al. (2004)